Alternative methods for direct kinematic analysis of a parallel robot for ankle rehabilitation

This work deals with the direct kinematic analysis of a parallel robot for ankle rehabilitation. The problem consists of solving a set of nonlinear equations derived from the closure equations of the closed kinematic chains which form the parallel architecture of the robot. The Newton-Rhapson method is often used for this kind of problem. However, the convergency of this method strongly depends on the initial conditions chosen for the iterative algorithm. Moreover, this method converges to only one of particular solution where many are possible. To overcome these disadvantages, two alternative numerical methods are proposed. Newton-Homotopy and Sylvester dialytic methods are implemented and the obtained results are discussed.